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Find the locus of the points represen...

Find the locus of the points representing the complex number `z` for which`|z+5|^2=|z-5|^2=10.`

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`|z+5|^(2)-|z -5|^(2) = 10`
`or (z+5) (bar z + 5) -(z -5) (bar z -5) =10`
`or 5(z + barz) + 25 + 5(z +barz) -25 = 10`
`or 2xx 2x = 2`
`or x = (1)/(2)`
Which is the equation of the a straight line.
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